Calculating volume of body enclosed by surfaces x 2 </msup> + y

Damon Stokes

Damon Stokes

Answered question

2022-06-19

Calculating volume of body enclosed by surfaces
x 2 + y 2 = 9; (cylinder)
x + y + z = 10
z = 0

Answer & Explanation

Colin Moran

Colin Moran

Beginner2022-06-20Added 21 answers

In cylindrical coordinates, the volume integral is
V = A z ( x , y ) d x d y = 0 2 π 0 3 ( 10 r cos θ r sin θ ) r d r d θ = 90 π
Edit:
V = 0 3 d r 0 2 π ( 10 r r 2 cos θ r 2 sin θ ) d θ
= 0 3 ( 20 π r r 2 sin θ | 0 2 π + r 2 cos θ | 0 2 π ) d r
= 0 3 ( 20 π r + 0 + 0 ) d r = 20 π 0 3 r d r = 90 π

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